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The purpose of this paper is twofold. As the first goal, we show that three different classes of random walks are counted by the Pell numbers. The calculations are done using a convenient technique that involves the Riordan group. This leads to the second goal, which is to demonstrate this convenient technique. We also construct bijections among Pell,(More)
Riordan matrix methods and manipulation of various generating functions are used to find curious relations among the Catalan, central binomial, and RNA generating functions. In addition, the Wilf-Zeilberger method is used to find identities where the gamma function and Catalan numbers are expressed in terms of the Gauss hy-pergeometric function. As a(More)
Some probabilistic results on simple sequence repeats (SSRs) in DNA sequences are derived and used to quantify the nonrandomness of SSRs as an index of nonrandomness. The applicability of the index of nonrandomness is illustrated using several examples from the literature on selected human diseased genes.
The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete(More)
Riordan matrix methods and properties of generating functions are used to prove that the entries of two Catalan-type Riordan arrays are linked to the Chebyshev poly-nomials of the first kind. The connections are that the rows of the arrays are used to expand the monomials (1/2) (2x) n and (1/2) (4x) n in terms of certain Chebyshev poly-nomials of degree n.(More)
Evidence is presented suggesting, for the first time, that the protein foldability metric sigma = (T(theta)-T(f))/T(theta), where T(theta) and T(f) are, respectively, the collapse and folding transition temperatures, could be used also to measure the foldability of RNA sequences. These results provide further evidence of similarities between the folding(More)
Purdue's focus is on visualization sciences, and Rutgers' focus is on data sciences, these two CVADA components are working closely on a number of activities, projects, and programs (Command, Control, and Interoperability Center for Advanced Data Analysis, 2013). Excellence perform critical research and development activities to provide the necessary(More)